# Math Help - probability problem

1. ## probability problem

The arrival of trucks on a receiving dock is a Poisson process with a mean arrival rate of two per hour.
(a) Find the probability that exactly 6 trucks arrive in a two-hour period.
(b) Find the probability that the time between two successive arrivals will be more than 3 hours.

Thanks!!

2. Poisson Probabilities are a matter of plugging into the formula.

$\lambda\;=\;2\;per\;hour$
n = 6/2 hours = 3 per hour

Calculate it. Let's see what you get.

For the second, Poisson Wait Times are Exponential. Let's see what you get.

3. I have a nearly identical question to this, for part (b) since the inter-arrival times are exponentially distributed would it be:

$\lambda = 2(3) = 6$ for your rate, then you would have:

$\int_3^\infty \lambda e^{-\lambda t} dt = \int_3^\infty 6 e^{-6 t} dt$ ?